Resumen de Automorphisms and examples of compact non-Kähler manifolds

Gunnar Þór Magnússon

• If f is an automorphism of a compact simply connected Kähler manifold with trivial canonical bundle that fixes a Kähler class, then the order of f is finite. We apply this well known result to construct compact non-Kähler manifolds. These manifolds contradict the abundance and Iitaka conjectures for complex manifolds.